interface damping in blade attachment region
Transcription
interface damping in blade attachment region
INTERFACE DAMPING IN BLADE ATTACHMENT REGION A THESIS SUBMITTED TO THE INDIAN INSTITUTE OF TECHNOLOGY, DELHI for the Award of the Degree of DOCTOR OF PHILOSOPHY BY MOHAMMED ABDUL WASAY USMANI DEPARTMENT OF MECHANICAL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY, DELHI APRIL, 1986 CERTIFICATE This is to certify that the thesis entitled "INTERFACE DAMPING IN BLADE ATTACHMENT REGION" being submitted by Mr. M. A . W. Usmani to the Indian Institute of Technology, Delhi (India) for the award of the Degree of Doctor of Philosophy in Mechanical Engineering Department, is a record of bonafide research work carried out by him under our supervision and guidance. The thesis work, in our opinion, has reached the standard fulfilling the requirements for the Doctor of Philosophy Degree. The research report and the results presented in this thesis have not been submitted in part or full to any other University or Institute for the award of any degree or diplorra . •s ,e( Prof. C. V. Ramakrishnan Prof.J.S.Rao Department of Applied Mechanics Department of Mechanical Engineering Indian Institute of Technology, Delhi.Indian Institute of Technology, Delhi. ACKNOWLFDUMFNTS The author wishes to express his deep sense of gratitude and indebtness to Prof. J.S. Rao of Mechanical Engineering Department and Prof. C.V. Ramakrishnan of Applied Mechanics Department for their inspiring technical guidence, active supervision and constant help at all stages of the research work. The author also wishes to place on record his sincere heart felt thanks to Prof. J.A. Munir, Prof. S.R. Khan, Prof. S.H. Mohsin, Dr. S. Tarique Jilani and Iqbal Mian of Mechanical Engineering Department of Aligarh Muslim University for their help and encouragement. In this research work which has spanned over a long . duration, it is impossible to acknowledge the help of all my colleagues and friends. However special thanks to Mr. I.A. Khan who made my stay comfortable at I.I.T. during the closing stages of this work. Thanks are also due to Mr. B.B. Arora, Mr. N.C. Saraswat and Mr. Ashok Vashistha for their assistance in the preparation of this thesis. Words can not express my gratitude to Afroze, my wife, for her help, encouragement, understanding and patience during my preoccupation with the research activity. Samina, Rafey and Uzma my children deserve special thanks as they were deprived of the usual attention due to author's absence from home. ,()C i M.A.W. Usmani ABSTRACT -------Energy dissipation is a major blade design criterion since damning limits the blade resonant amnlituies an(: stresses which may develop under steady oneratini7 conditirIns ',7ith harmonic forcing input. T3lade damning is therefore a desirable structural nronerty which helps to reduce the nossihility of blade damage from metal fatigue. 7\ major contribution of damning in a free standing blade arises from the interface.slin that take niece in the blade root junction. This thesis is concerned 4ith the estimation of damning in the blade disk junction. The nresent work addresses the nroblem of evaluation of root damning using analytical and exnerimental nrocedures. To study the nroblem analytically, the finite element method has been made use of and to simulate the blade - root behaviour, the dynamic contact nrohlem under the action of centrifugal force and a lateral load is analysed using a time marching nrocedure. 71 general nurnose comnuter nrogram consisting of a main nrogram and twenty eight other segments has•been develoned. The program is very efficient since only the equations corresponding to the contact nodes, loaded noded and the nodes which leave contact are set un at every iterative sten within a. time interval. The nrogram is canahle of handling inclined contact surfaces and the nresence of clearances. (iv) k free vibration analysis of a blade with ?striddle-T type root junction has been ,nade to deter-line the lcflrath'lic decrernent at successive ti'''e stens. To estimate the true behaviour, the initial disnlace,rents have been obtaini by solving static contact nroble-I. The amain-( ratio has been obtained as a function of centrifugn.1 load and ti') dis-)lacements. A test rig to determine the damning of a blade-root is designed and fabricated uqinr thermal_ coolinct to si.)-lulate the centrifugal load. The tests can be carried out in air as well as in vacuum. 7xperiments have been conducted to estimate blade damning and atter-1--)ts have been made to correlate it with the theoretical investi-lations !nentioned earlier. While the qualitative trend is 17ound to be alricrht, there is considerable deviation from the theoretical nrediction on account of the oractical conditions in which the blade is mounted. The thesis ends with a detailed summary of conclusions and suggestions for future research. (v ) 1TE'1T S i Certificate Acknowledgements Abstract' Contents CliiVnE List of Pigures ix List of Photogranhs xii List of 'Symbols xiii -1 INT7ODUCTION AND LTTE”ATTME sur2VEm1-15 1.1 Introduction 1 1.2 general Tteview of 'Thee Vibration2 Analysis of Turbine 731ades 1.3 Pole of namning in Iribration and Analytical Methods of Determining It. 1.3.1 Source of D,amning in steam Turbine 91ading 1.4 review of Work .on T)amninq of. Turbomachine3 Blades 1.5 Finite Element Analysis or Contact problem12 1.6 Scone of present Invstigations13 1.7 organisation of the Thesis14 CHAPTEP -2 ANALYSTS OF STATIC CONTACT T",(VIT,T7416-4 3 2:1 Introduction 16 2.2 The Finite Element method 17 2.2.1 Ouadratic Tsonr)rametric Elements22 (vi) R age 2.3 Method of Analysis of Static Contact 7)roblem 22 2.4 Analysis of 31ade Root-Disk Junction28 For Centrifugal Force 2.4.1 Finite Element Discretization29 2.4.2 Boundary Conditions30 2.4.3 Results of Analysis of Blade-Disk30 Assembly. 2.4.3.1 Results of T-Root Junction31 2.4.3.2 Results of Straddle T-root31 Junction 2.5 Conclusions 31 CHAPTER -3 MODELLING OF DYNAMIC CONTACT PROBLE 44-60 3.1 Introduction 44 3.2 Governing 77untion7 44 Wilson-0 Method 47 3.4 Derivation of the (;overninrr Equations 49 for the Subregion 3.5 Simulation of Openinl 52 3.6 Simulation of Slip 53 3.7 Contact Along Inclined Surfaces54 3.8 Efficient Computation of Condensed Equations 55 3.9 Numerical Procedure 57 3.10 Conclusions 59 CHAPTER -4 DEVELOPMENT OF COMPUTER PP0GRAM 61-81 4.1 Introduction 61 Page 4.2 General Organisation of the Program61 4.2.1 Data Processor 62 4.2.2 Flexibility Matrix Analyser63 '4.2.2.1 Computation of Element64 Property Matrices 4.2.2.2 Computation of Load Vector66 4.2.2.3 Comoutation of P-IS For66 Dynamic Terms 4.2.2.4 - Static Condensation And67 Inversion 4.2.3 Contact Solver 68 4.2.4 Elastic 71nalyser 69 4.3 Test Problems And Results 70 4.3.1 Cantilever Under Suddenly Apnlied70 Load 72 4.3.2 Suddenly 7\pplied Load in a Cantilever with part of the body having high rigidity 4.3.3 Dynamic Modelling of. Joint 0nening72 and Closing and Slip CHAPTER -5 FINITE ELEMENT MODELLING OF ROOT DAMPING82-106 5.1 Introduction 82 5.2 Finite Element Modelling 82 84 5.3 Response of A. Cantilever. Ilade Under Suddenly Aoolied Load 85 5,4 Effect of Centrifugal Load 87 5.5 Effect of. Coefficient of Eriction 88 5.6 Effect of Lateral Load (viii) Page 5.7 Effect of Root qeometry go 5.8 Discussion and Conclusions90 CHAPTER -6 EXPERIMENTAL STUDIES ON ROOT DAMPINry107-15Z 6.1 Introduction 107 6.2 Methods of Damnin7 Estimation in Dlade Root107 .6.2.1 Logarithmic Decrement Method107 6.2.2 Half Rower (3anftiidth) Method109 6.3 Exnerimental Setun 109 6.4 Details of Test Rig 110 6.4.1 Dimensional Mismatch112 6.5 Instrumentation 113 6.5.1 Measurements for Centrifuclal Meld113 6.5.2 Measurements of Transient Decay114 6.5.3 Instrumentation for Excitation115 in Vacuum 6.6 Discrintion of the Nssembled Setun115 6.7 Test Procedure 115 6.8 Test in Tir 117 6.9 Test in Vacuum 118 .6.10 Results and Discussions 119 CHAPTER -7 CONCLUSION 153-155 • 7.1 Scone of_' qork and Sucr7estion for Future154 Research REFERENCES 156-167 APPENDIX 168-169